SOLUTION: Jack can build a wall on his own in 16 hours. Jill can build the same wall in 12 hours working alone.. If they work together they can build the wall in 8 hours, but because theyso

Question 761804: Jack can build a wall on his own in 16 hours. Jill can build the same wall in 12 hours working alone.. If they work together they can build the wall in 8 hours, but because theysometimes get in each others way, they lay 16 bricks less per hour between them than if they didn�t get in each other�s way. So the question is� How many bricks are there in the wall?
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Let b = the interference rate when Jack and Jill build together.
Without interferences, you expect the combined rate to be 1/16+1/12,
but in the situation, the actual rate is combined with b jobs per hour in the opposite direction:

where .
LCD is 2*2*2*2*3, so simplifying and here omitting the steps,
(Multiplying both sides first by the LCD)

jobs per hour but IN THE OPPOSITE DIRECTION.

That is 1 job per 48 hours as an interference. This is the same ratio as the 16 bricks per hour.

We have a proportion.
{16 bricks / 1 hour} = { 1 job / 48 hours }.
We want to increase BOTH numerator and denominator on the left so that we match the 48 hour value. We do it like this:

to obtain the same denominator of 48 hours.
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RESULT: 768 bricks are in the whole job, one wall.
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